a review - Acta Technica Corviniensis

ROLE OF METAMODELING
Detailed research has been carried out in using
metamodeling techniques in design optimization.
This research includes experimental design methods,
metamodel types, model fitting techniques,
application of metamodels in design optimization and
reliability based design. Through literatures it has
become clear that metamodeling provides a decision
support role for all design engineers. The supporting
functions that metamodels can provide are listed
here with reference to the literatures [6]:
a) Model approximation-models which replace the
computationally expensive codes,
b) Design space exploration-understanding the design
problem in the whole design space by using
metamodels,
c) Optimization – e.g., global optimization, multiobjective
optimization, multidisciplinary
optimization, probabilistic optimization and so on.
Metamodels are integrated to the above
optimization problems to reduce the
computational burden.
d) Reliability based design- Reliability assessment is
the prime function for Reliability based design.
Metamodels are used to approximate the
expensive constraint functions, or the limit state
function.
Figure 1 illustrates the support afforded by
metamodels.
Figure 1. Support provided by metamodels
The evolution of metamodel based analysis is
summarized in figure 2, which shows the number of
publications related to metamodels over the past
three decades. This data was obtained using the
‘Scirus scientific research tool’ where we searched
for occurrences of the word: “metamodels”(during
May 2011). Figure 3 illustrates the number of
publications reporting the use of metamodels in
design optimization and reliability analysis
applications. For each application, the search was
made with the following words: metamodels AND
design optimization or metamodels AND reliability
analysis.
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Figure 2. No. of publications, from 1980 - 2011
ACTA TECHNICA CORVINIENSIS – Bulletin of Engineering
Figure 3. Metamodels in design optimization and
reliability analysis
METAMODELING
Metamodeling involves (a) Selection of experimental
design for generating data, (b) Selection of model to
represent the data, and (c) fitting the observed data
using the model. There are several options for each
of these steps, as shown in figure 2. For example,
response surface methodology usually employs
central composite designs, polynomials and
regression analysis.
Experimental designs
An experimental design (or Design of
experiments) is an organized method to determine
the relationship between the different factors
affecting the output of a process. As indicated in
Figure 4, there are several experimental design
methods. Design of Experiments includes the design
of all information-gathering exercises where
variation is present, usually under the full control of
the experimenter. Often the experimenter is
interested in the effect of some process or
intervention on some objects. Design of experiments
is a discipline that has very broad application.
Figures 4. Types of Metamodelling Techniques
Classical design and analysis of physical experiments
accounts the random variation by spreading the
sample design points in the design space and by
taking replicate design points. Commonly used
classical designs are factorial or fractional factorial,
Central Composite Design(CCD), Box-Behnken design,
Plackett-Burman design. Also classical designs spread
the sample points around the boundaries and leave a
few at the center of the design space. Sacks, et al.
[7] stated that as computer experiments involve
mostly systematic error rather than random error, a
good experimental design tends to fill the design
space. They also stated that to classical designs, e.g.
CCD can be inefficient or even inappropriate for
deterministic computer codes. Jin, et al. [8] also
confirms that experimental designs for deterministic
2013. Fascicule 2 [April–June]